Sequence alignment is a way of arranging primary sequences of DNA, RNA, or protein to identify regions of similarity. This region may be a consequence of functional, structural, or evolutionary relationships between the sequences. An algorithm is proposed for finding approximate local similarities in DNA sequences (AFALS-N). This algorithm is capable of finding the similarity between two sequences by generating all the possible words in the first sequence, then finding the exact matches in the second sequence. The selection of the obtained results is essential to reduce the number of possible results that in turn reduces the searching time. Results show that the proposed algorithm has reduced the searching time to an average of 20% in regard to PatternHunter algorithm. The objective of this work was evident by maintaining balance between the execution time and the size of seeds and the sensitivity. Improved execution time with 66% of sensitivity are obtained with the same word size as those used in other algorithms.